Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.Comment: 31 pages, minor misprints are correcte

Semiparametric analysis to estimate the deal effect curve

The marketing literature suggests several phenomena that may contribute to the shape of the relationship between sales and price discounts. These phenomena can produce severe nonlinearities and interactions in the curves, and we argue that those are best captured with a flexible approach. Since a fully nonparametric regression model suffers from the curse of dimensionality, we propose a semiparametric regression model. Store-level sales over time is modeled as a nonparametric function of own-and cross-item price discounts, and a parametric function of other predictors (all indicator variables). We compare the predictive validity of the semiparametric model with that of two parametric benchmark models and obtain better performance on average. The results for three product categories indicate a.o. threshold- and saturation effects for both own- and cross-item temporary price cuts. We also show how the own-item curve depends on other items’ price discounts (flexible interaction effects). In a separate analysis, we show how the shape of the deal effect curve depends on own-item promotion signals. Our results indicate that prevailing methods for the estimation of deal effects on sales are inadequate.

Towards Formal Interaction-Based Models of Grid Computing Infrastructures

Grid computing (GC) systems are large-scale virtual machines, built upon a massive pool of resources (processing time, storage, software) that often span multiple distributed domains. Concurrent users interact with the grid by adding new tasks; the grid is expected to assign resources to tasks in a fair, trustworthy way. These distinctive features of GC systems make their specification and verification a challenging issue. Although prior works have proposed formal approaches to the specification of GC systems, a precise account of the interaction model which underlies resource sharing has not been yet proposed. In this paper, we describe ongoing work aimed at filling in this gap. Our approach relies on (higher-order) process calculi: these core languages for concurrency offer a compositional framework in which GC systems can be precisely described and potentially reasoned about.Comment: In Proceedings DCM 2013, arXiv:1403.768

Reduced Memory Footprint in Multiparametric Quadratic Programming by Exploiting Low Rank Structure

In multiparametric programming an optimization problem which is dependent on a parameter vector is solved parametrically. In control, multiparametric quadratic programming (mp-QP) problems have become increasingly important since the optimization problem arising in Model Predictive Control (MPC) can be cast as an mp-QP problem, which is referred to as explicit MPC. One of the main limitations with mp-QP and explicit MPC is the amount of memory required to store the parametric solution and the critical regions. In this paper, a method for exploiting low rank structure in the parametric solution of an mp-QP problem in order to reduce the required memory is introduced. The method is based on ideas similar to what is done to exploit low rank modifications in generic QP solvers, but is here applied to mp-QP problems to save memory. The proposed method has been evaluated experimentally, and for some examples of relevant problems the relative memory reduction is an order of magnitude compared to storing the full parametric solution and critical regions

Parameterised Multiparty Session Types

For many application-level distributed protocols and parallel algorithms, the set of participants, the number of messages or the interaction structure are only known at run-time. This paper proposes a dependent type theory for multiparty sessions which can statically guarantee type-safe, deadlock-free multiparty interactions among processes whose specifications are parameterised by indices. We use the primitive recursion operator from G\"odel's System T to express a wide range of communication patterns while keeping type checking decidable. To type individual distributed processes, a parameterised global type is projected onto a generic generator which represents a class of all possible end-point types. We prove the termination of the type-checking algorithm in the full system with both multiparty session types and recursive types. We illustrate our type theory through non-trivial programming and verification examples taken from parallel algorithms and Web services usecases.Comment: LMCS 201

Resource use efficiency of US electricity generating plants during the SO2 trading regime: A distance function approach.

This paper measures resource use efficiency of electricity generating plants in the United States under the SO2 trading regime. Resource use efficiency is defined as the product of technical efficiency and environmental efficiency, where the latter is the ratio of good output (electricity) to bad output (SO2) with reference to the best practice firm, i.e., one that is producing an optimal mix of good and bad outputs. This concept of environmental efficiency is similar to that of output oriented allocative efficiency. Using output distance functions we compare three methods for the calculation of resource use efficiency, namely, stochastic frontier analysis (SFA), deterministic parametric programming and nonparametric linear programming. This paper reveals the strengths and weaknesses of these methods for estimating efficiency. Both SFA and linear programming approaches can estimate the efficiency scores. For plants in the dataset the overall geometric mean of the three methods for technical efficiency, environmental efficiency and resource use efficiency is 0.737, 0.335 and 0.248, respectively. The rank correlation coefficient between technical efficiency, environmental efficiency and resource use efficiency is 0.213, 0.617 and 0.877, respectively. The regression analyses of performance across plants shows units in phase I of the SO2 trading programme are negatively related to measures of economic and environmental performance. This suggests that the market for SO2 allowances, per se, may not be minimizing compliance cost. We also find that a decrease in SO2 emission rates not only increases environmental efficiency but also leads to an increase in resource use efficiency. This finding concurs with the hypothesis that enhancement in the environmental performance of a firm leads to an increase in its overall efficiency of resource use as well.Technical efficiency ; Environmental efficiency ; Resource-use efficiency ; Distance functions ; SO2 allowance program

Hierarchies of Inefficient Kernelizability

The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However, there are also some issues that are not addressed by this framework, including the existence of Turing kernels such as the "kernelization" of Leaf Out Branching(k) into a disjunction over n instances of size poly(k). Observing that Turing kernels are preserved by polynomial parametric transformations, we define a kernelization hardness hierarchy, akin to the M- and W-hierarchy of ordinary parameterized complexity, by the PPT-closure of problems that seem likely to be fundamentally hard for efficient Turing kernelization. We find that several previously considered problems are complete for our fundamental hardness class, including Min Ones d-SAT(k), Binary NDTM Halting(k), Connected Vertex Cover(k), and Clique(k log n), the clique problem parameterized by k log n